I unfortunately don't have a PC. I just tried plugging in my mac at it shows that the monitor is indeed capable of going to 144hz (if that means anything).
PS5 has all of what you just said. Here's what happened when I tried playing around with it:
- Low latency mode (says that my "Tv doesn"t support this mode")
- VRR (says that my "Tv doesn"t support this mode")
- HRD (I tried turning it on and off to see if it changed anything, but nothing really)
- Refresh Rate: I set it to automatic 120hz for games that do support it. NHL doesn't so I don't really mess with that.
I didn't take this screenshot, but it shows basically all the options I have.

As for the monitor's settings, I did try to mess around with all the sliders you mentioned below. But nothing really came from it.
I feel like there might be something wrong with my Ps5...it feels way more difficult than it should be to just find a monitor on which I can play the game smoothly.
I often play at my best friend's, who plays on a Samsung TV and the game is the smoothest I've ever played it.